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y=(arccosx)^ln2^x
Derivada de la función/ arccos/ y=(arccosx)^ln2^x

Derivada de y=(arccosx)^ln2^x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Solución

Ha introducido [src] 
            x   
         log (2)
(acos(x))
acos⁡log⁡(2)x(x)\operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)} 
acos(x)^(log(2)^x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(log⁡(2)x)+1)log⁡(2)xlog⁡(2)x\left(\log{\left(\log{\left(2 \right)}^{x} \right)} + 1\right) \log{\left(2 \right)}^{x \log{\left(2 \right)}^{x}}

  2. Simplificamos:

    (xlog⁡(log⁡(2))+1)log⁡(2)xlog⁡(2)x\left(x \log{\left(\log{\left(2 \right)} \right)} + 1\right) \log{\left(2 \right)}^{x \log{\left(2 \right)}^{x}}

Respuesta:

(xlog⁡(log⁡(2))+1)log⁡(2)xlog⁡(2)x\left(x \log{\left(\log{\left(2 \right)} \right)} + 1\right) \log{\left(2 \right)}^{x \log{\left(2 \right)}^{x}}

Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
            x    /                                            x         \
         log (2) |   x                                     log (2)      |
(acos(x))       *|log (2)*log(acos(x))*log(log(2)) - -------------------|
                 |                                      ________        |
                 |                                     /      2         |
                 \                                   \/  1 - x  *acos(x)/
(log⁡(2)xlog⁡(log⁡(2))log⁡(acos⁡(x))−log⁡(2)x1−x2acos⁡(x))acos⁡log⁡(2)x(x)\left(\log{\left(2 \right)}^{x} \log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{\log{\left(2 \right)}^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}
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Segunda derivada [src] 
            x            /                                                                     2                                                                                \
         log (2)    x    |        1            /                                    1         \     x         2                                 x               2*log(log(2))   |
(acos(x))       *log (2)*|------------------ + |log(acos(x))*log(log(2)) - -------------------| *log (2) + log (log(2))*log(acos(x)) - ------------------- - -------------------|
                         |/      2\     2      |                              ________        |                                                3/2              ________        |
                         |\-1 + x /*acos (x)   |                             /      2         |                                        /     2\                /      2         |
                         \                     \                           \/  1 - x  *acos(x)/                                        \1 - x /   *acos(x)   \/  1 - x  *acos(x)/
(−x(1−x2)32acos⁡(x)+(log⁡(log⁡(2))log⁡(acos⁡(x))−11−x2acos⁡(x))2log⁡(2)x+log⁡(log⁡(2))2log⁡(acos⁡(x))+1(x2−1)acos⁡2(x)−2log⁡(log⁡(2))1−x2acos⁡(x))log⁡(2)xacos⁡log⁡(2)x(x)\left(- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \left(\log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right)^{2} \log{\left(2 \right)}^{x} + \log{\left(\log{\left(2 \right)} \right)}^{2} \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{1}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 \log{\left(\log{\left(2 \right)} \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \log{\left(2 \right)}^{x} \operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}
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Tercera derivada [src] 
            x            /                                                3                                                                                                                       2                  2                                                                                                                                                                                                                 \
         log (2)    x    |/                                    1         \     2*x         3                                 1                     2                     3*x                   3*x              3*log (log(2))          x    /                                    1         \ /          1               2                                 x               2*log(log(2))   \     3*log(log(2))        3*x*log(log(2))  |
(acos(x))       *log (2)*||log(acos(x))*log(log(2)) - -------------------| *log   (2) + log (log(2))*log(acos(x)) - ------------------- - -------------------- - ------------------- - ------------------- - ------------------- - 3*log (2)*|log(acos(x))*log(log(2)) - -------------------|*|- ------------------ - log (log(2))*log(acos(x)) + ------------------- + -------------------| + ------------------ - -------------------|
                         ||                              ________        |                                                  3/2                   3/2                     2                    5/2              ________                     |                              ________        | |  /      2\     2                                          3/2              ________        |   /      2\     2              3/2        |
                         ||                             /      2         |                                          /     2\              /     2\        3      /      2\      2      /     2\                /      2                      |                             /      2         | |  \-1 + x /*acos (x)                               /     2\                /      2         |   \-1 + x /*acos (x)   /     2\           |
                         \\                           \/  1 - x  *acos(x)/                                          \1 - x /   *acos(x)   \1 - x /   *acos (x)   \-1 + x / *acos (x)   \1 - x /   *acos(x)   \/  1 - x  *acos(x)             \                           \/  1 - x  *acos(x)/ \                                                   \1 - x /   *acos(x)   \/  1 - x  *acos(x)/                        \1 - x /   *acos(x)/
(−3x2(1−x2)52acos⁡(x)−3x(x2−1)2acos⁡2(x)−3xlog⁡(log⁡(2))(1−x2)32acos⁡(x)+(log⁡(log⁡(2))log⁡(acos⁡(x))−11−x2acos⁡(x))3log⁡(2)2x−3(log⁡(log⁡(2))log⁡(acos⁡(x))−11−x2acos⁡(x))(x(1−x2)32acos⁡(x)−log⁡(log⁡(2))2log⁡(acos⁡(x))−1(x2−1)acos⁡2(x)+2log⁡(log⁡(2))1−x2acos⁡(x))log⁡(2)x+log⁡(log⁡(2))3log⁡(acos⁡(x))+3log⁡(log⁡(2))(x2−1)acos⁡2(x)−3log⁡(log⁡(2))21−x2acos⁡(x)−1(1−x2)32acos⁡(x)−2(1−x2)32acos⁡3(x))log⁡(2)xacos⁡log⁡(2)x(x)\left(- \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} - \frac{3 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} - \frac{3 x \log{\left(\log{\left(2 \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \left(\log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right)^{3} \log{\left(2 \right)}^{2 x} - 3 \left(\log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \log{\left(\log{\left(2 \right)} \right)}^{2} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{2 \log{\left(\log{\left(2 \right)} \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \log{\left(2 \right)}^{x} + \log{\left(\log{\left(2 \right)} \right)}^{3} \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{3 \log{\left(\log{\left(2 \right)} \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{3 \log{\left(\log{\left(2 \right)} \right)}^{2}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}}\right) \log{\left(2 \right)}^{x} \operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}
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Gráfico
Derivada de y=(arccosx)^ln2^x
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